\chapter[Linear Algebra \\ \textnormal{\emph{Lectured in Michaelmas \oldstylenums{2021} by \textsc{Prof.\ P.\ Raphael}}}]{Linear Algebra}
\emph{\Large Lectured in Michaelmas \oldstylenums{2021} by \textsc{Prof.\ P.\ Raphael}}

Linear algebra is the field of study that deals with vector spaces and linear maps.
A vector space can be thought of as a generalisation of \( \mathbb R^n \) or \( \mathbb C^n \), although they can be based off any field (not just \( \mathbb R \) or \( \mathbb C \)), and may have infinitely many dimensions.
In this course, we mainly study finite-dimensional vector spaces and the linear functions between them.
Any linear map between finite-dimensional vector spaces can be encoded as a matrix.
Such maps have properties such as their trace and determinant, which can be easily obtained from a matrix representing them.
As was shown for real matrices in Vectors and Matrices, if the determinant of a matrix is nonzero it can be inverted.

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